P. Brass, W. Moser, J. Pach:
Research Problems in Discrete Geometry
Springer, New York, 2005
Facsimile edition: China Science Press, Beijing, 2006
Japanese translation: Springer, Tokyo, 2009
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Although Discrete Geometry has a rich history extending more than 150 years, it abounds in open problems that
even a high-school student can understand and appreciate. Some of these problems are notoriously difficult and
are intimately related to deep questions in other fields of mathematics. But many problems, even old ones, can
be solved by a clever undergraduate or a high-school student equipped with an ingenious idea and the kinds of
skills used in a mathematical olympiad.
"Research Problems in Discrete Geometry" is the result of a twenty-five year old project initiated by the
late Leo Moser. It is a collection of more than 500 attractive open problems in the field, many of which can
be understood without extensive preparation. The largely self-contained chapters provide a broad overview of
discrete geometry, along with historical details and the most important partial results related to these
problems. This book is intended as a source book for both professional mathematicians and graduate students
who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who
would like to get involved in mathematical research.
Important features include:
Peter Brass is Associate Professor of Computer Science at the City College of New York. William O. J. Moser
is Professor Emeritus at McGill University. Janos Pach is Distinguished Professor of Computer Science at The
City College of New York, Research Professor at the Courant Institute, NYU, and Senior Research Fellow at the
- More than 500 open problems, some old, others new and never before published;
- Each chapter divided into self-contained sections, each section ending with an extensive
- A great selection of research problems for graduate students looking for a dissertation topic;
- A comprehensive survey of Discrete Geometry, highlighting the frontiers and future of research;
- More than 150 figures;
- A Preface to an earlier version written by the late Paul Erdos.
|Table of Contents
|Preface by Erdős to an earlier version